Estimators for the difference in means/mediansEstimators for the difference in means/medians of related samples and their properties and assumptions.

Estimator	Purpose
Mean difference	Estimate the difference between the means.
Standardized mean difference	Estimate the standardized difference between the means. Cohen's d is the most popular estimator using the difference between the means divided by the pooled sample standard deviation. Cohen's d is a biased estimator of the population standardized mean difference (although the bias is very small and disappears for moderate to large samples) whereas Hedge's g applies an unbiasing constant to correct for the bias.
Median difference	Estimate the median of the differences.
Hodges-Lehmann location shift	Estimate the shift in location. A shift in location is equivalent to a difference between means/medians when the distribution of the differences is symmetric. Symmetry is quite often inherently satisfied for paired data.